Question

solve the equation. log 25 - log 2x = 1
x = (type an integer or a decimal.)

Explanation:

Step1: Use log rule $\log a-\log b=\log\frac{a}{b}$

$\log\frac{25}{2x}=1$

Step2: Rewrite in exponential form

Since $\log_{10}y = x$ is equivalent to $y = 10^x$, we have $\frac{25}{2x}=10^1 = 10$.

Step3: Solve for $x$

Cross - multiply: $25 = 10\times2x$, so $25 = 20x$. Then $x=\frac{25}{20}=\frac{5}{4}=1.25$.

Answer:

$1.25$